In hyperspectral image (HSI) classification task, semisupervised graph convolutional network (GCN)-based methods have received increasing attention. However, two problems still need to be addressed. The first is that the initial graph structure in the GCN-based methods is not sufficiently flexible to encode the homogenous structure similarity of HSI pixels when facing the complex scenarios induced by the spatial variability. Another problem is that the input (graph structure) and output (output features) of the GCN-based methods are separated with a "single pass" procedure, which is a suboptimal problem for HSI classification because it does not flexibly optimize the graph construction with a feedback method via output features. In this article, a novel spatial-spectral unified adaptive probability GCN (SSAPGCN) method is proposed for HSI classification. First, considering the homogeneous structural similarity of the pairwise relationships of HSI pixels, this article combines the inherent spectral information and spatial coordinates to obtain the spatial-spectral adaptive probability graph (SSAPG) structure, which can capture the probabilistic connectivity between each pair of the homogeneous HSI pixels. Second, the SSAPG structure and GCN model are combined into a unified framework to a daptively learn both the graph structure and the output features simultaneously with feedback. Finally, the proposed SSAPGCN method with two layers is evaluated on four public HSI datasets to demonstrate its superiority over different classification methods in terms of two evaluation metrics, the overall accuracy (OA) and kappa coefficient (KC), especially with small training sample sizes.